The present invention relates to an improved iterative controlled adaptive digital filter which is stable in operation and has improved phase response characteristics. The present filter is used for instance as a predictive filter in an adaptive PCM (ADPCM) modulator and/or demodulator. According to the present invention, only the relative location of a pair of solutions of a transfer function on a unit circle on a Z.sup.-1 plane is monitored, while a prior art monitors the values themselves of the solutions (zero, and pole) of denominator and numerator of transfer function of a non-recursive digital filter which has a feedback loop.
FIG. 1 shows a block diagram of an ADPCM system which is one of the applicatoins of the present invention. In FIG. 1, the numeral 0 is an A/D converter to convert an analog signal (for instance, voice signal or picture signal) at the input terminal 11 to a digital form, 1,4 and 7 are adders, 2 is a quantizer for converting an input digital signal to a PCM code, 3 and 6 are inverse-quantizers which demodulates a PCM signal, 5 and 8 are filters, 9 is a D/A converter for converting a digital signal to an analog form, and 11 through 18 are terminals. An analog signal at the input terminal 11 is converted to a digital form by the A/D converter 0. A digital signal s.sub.k (k shows time) is applied to the adder 1 which adds the expected signal s.sub.k to the input signal s.sub.k and provides the sum which is the error signal e.sub.k. The error signal e.sub.k is quantized by the quantizer 2 and is transmitted to an external circuit through the output terminal 13. The signal at the terminal 13 is reproduced to an error signal e.sub.k by the inverse-quantizer 3 and is applied to the adder 4 which adds said predicted value s.sub.k and the sum is the reproduced value s.sub.k.
Similarly, the signal at the output terminal 13 is transmitted to a reception side or a demodulation side. Noise might be added to the signal during the signal is transmitted to the reception side. In a reception side, the reception signal at the input terminal 16 is reproduced to the reproduce signal s.sub.k by the inverse-quantizer 6, the adder 7 and the filter 8. Further, the output signal at the terminal 17 is converted to an analog form by the D/A converter 9.
FIG. 2 is a block diagram of a prior non-recursive digital filter for the filters 5 and 8 in FIG. 1. In FIG. 2, the symbol Z.sup.-1 is a delay circuit which provides the delay time T which is equal to the sampling period of the digital signal. The symbols .alpha..sub.1 through .alpha..sub.n are tap coefficients, and the value of them are iteratively adjusted according to an input signal so that the error signal e.sub.k becomes minimum.
It has been known that an all pole type filter is preferable for a speech signal. On the other hand, a filter which has not only a pole but also a zero point is preferable for multi-level digital signal which has quick change in both amplitude and phase.
However, a filter with both a pole and a zero point has not been used because that kind of filter is apt to oscillate and be affected by noise.
FIG. 3 shows a block diagram of an ADPCM system which includes both a pole and a zero point. In the figure, the numerals 19, 20, 21 and 22 are filters, 23 through 26 are terminals. Other symbols in FIG. 3 are the same as those of FIG. 1. The filters 19 through 22 are non-recursive filters with the structure of FIG. 2.
The transfer function H(Z.sup.-1) of the transmission side of FIG. 3 has the following form. EQU H(Z.sup.-1)=((1-H.sub.p (Z.sup.-1))/(1+H.sub.z (Z.sup.-1)) EQU =h.sub.p (Z.sup.-1)/h.sub.z (Z.sup.-1) (1)
The transfer function of the reception side is the inverse number of the equation (1). In FIG. 3, the transfer function of the filter between the terminals 12 and 13 is provided a zero point by the non-recursive filter 19, and a pole by the non-recursive filter 20. Therefore, the filter 19 is called a zero filter, and the filter 20 is called a pole filter. The reception side has a zero filter 21, and a pole filter 22.
Conventionally, it has been known that a prior filter of FIG. 2 is not stable in operation. Further, in a prior art, the response of the system is not stable for an input signal which has unexpected statistical nature, and/or noise, and further, the filter is apt to oscillate and/or the reproduced code has much code error.
In order to solve the above problem, one solution is to use a fixed filters 20 and 22 (only filters 19 and 21 are adaptive filters), and the other prior solution is to delete the filters 20 and 22, and that the filters 19 and 21 have the series connection of a plurality of dual quadratic element filters each of which has a pair of tap coefficients in a stable area. However, the former solution has the disadvantage that the adaptive capability and/or the redundancy compression capability is reduced. The latter solution has the advantage that the stable condition of the filter is satisfied, but, no mathematical algorithm for determining mutual relations between tap coefficients and solutions (pole and zero point) of each element filter. If the filters are adjusted so that an error signal becomes minimum, the convergence of solutions becomes slow and effect of a zero point becomes vague.